Fermat's Theorem

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Fermat's theorem

[′fer‚mäz ‚thir·əm]
The proposition that, if p is a prime number and a is a positive integer which is not divisible by p, then a p-1-1 is divisible by p.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Fermat’s Theorem


(or Fermat’s lesser theorem), a fundamental theorem of number theory. The theorem states that if p is a prime number and a is a whole number not divisible by p, then ap–1 – 1 is divisible by p—that is, ap–1 ≡ 1 (mod p). The theorem was set forth by P. Fermat without proof; the first proof was given by L. Euler.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
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